Interferometric measuring procedures can provide a highly accurate analysis of sample surfaces. Computer-assisted analysis of interferograms allows measuring resolutions perpendicular to the sample surface better than approximately 1:100 of the measuring-light's wavelength. However, interferometry can determine only relative differences between two sample surfaces. Absolute testing, i.e., the comparison of a sample surface relative to a mathematical plane, requires calibration of the interferometer so that deviations of the measuring surface itself, relative to the mathematical plane, are known with appropriate accuracy.
A known method for absolute testing of plane surfaces has been described by J. Schwider et al. in "Optica Acta, " Volume 13, Issue 2, pages 103-119 (1966), and by J. Schwider, in "Optica Acta," Volume 14, Issue 4, pages 389-400 (1967). It is based on the classical procedure of measuring double combinations of three plane surfaces in a Fizeau interferometer relative to each other where the plane surfaces are the reflectors of the interferometer. However, this method is limited by a reflectance problem relating to the inversion of the plane surfaces relative to the coordinate system of the recording camera, and absolute testing is possible only along a central straight line.
The just-named authors have improved this testing procedure to the extent that absolute testing of plane surfaces relative to a suitably selected mathematical plane may be carried out successively along as many central straight lines as desired and even along eccentric straight lines. To accomplish this, the plane surfaces must be rotated and shifted repeatedly about their surface normal by suitable angles relative with respect to each other; and after each rotation or shifting, an interferogram must be displayed and analyzed. For example, eleven interference images are required in order to test a sample on six central and nine eccentric straight lines. However, while this method permits absolute testing of the plane surfaces on a grid of straight lines, between the straight lines there are always regions where the sample surfaces remain unknown. Also, this prior art method requires that, at all times, two of the three samples must be transparent at the wavelength of the measuring light. Furthermore, any inadvertent tilting of the plane surfaces during rotation or shifting leads to erroneous analytical values.
It has been suggested that the reflectance problem referred to above could be avoided by using an auxiliary mirror to measure a total of four plane surfaces relative to each other. A more detailed investigation, however, has shown that this suggested method also provides absolute testing only along a single straight line.
The reflectance problem does not occur when global polynominal graphs are used as a basis for plane surfaces, and such a method for the surface absolute testing of plane surfaces is described in "Optical Engineering," Volume 23, page 379 (1984). However, since a global polynominal graph acts as a low-pass filter, a loss of spatial resolution must be accepted when using this prior art method.
Another known method for surface absolute testing of plane surfaces is the Ritchey-Common test described by F. M. Kuchel in "Summaries of the Papers Presented at the Optical Fabrication and Testing Workshop," Oct. 21 to 23, 1986, Seattle, pages 114-119. Like the Twyman-Green interferometer, this method is based on the autocollimation principle. Wavefront disturbances caused by the interferometer are initially determined during three separate method steps. During two additional method steps, a sample surface is inserted in the divergent measuring-beam path of the interferometer at different incident angles, and another interferogram is recorded in each case. These five interferograms can then be used to calculate the deviations of the sample surface from a mathematical plane. However, this analysis requires extensive mathematical computation due to the fact that (a) the equidistant pixel grid of the camera is projected on the sample surface in a non-equidistant grid, (b) the pixel spacing of the projected grid also varies as a function of the incident angle, and (c) the relation between the measured wavefront disturbance and the deviation of the sample surface from a mathematical plane also varies across the diameter of the measuring beam. Because of the inclined incidence of the divergent measuring beam, this method requires an extremely time-consuming conversion, by local interpolation, between the pixels of a total of three different pixel grids.
Therefore, the invention herein is directed to providing an interferometric method which solves the problems identified above, and which achieves the absolute surface testing of plane surfaces with high spatial resolution and a minimum of mathematical computation.